Civil Engineering Reference
In-Depth Information
20
L/d
= 25
E
p
/G
L
= 1000
r
= 0.75
n
= 0.3
18
16
s/d
= 2
14
12
s/d
= 3
10
8
s/d
= 5
6
4
s/d
= 10
2
Raft stiffness
0
0.1
1
10
Normalized width of pile group,
B/L
Figure 5.8
Normalized pile group stiffness for square groups of piles.
divided by average settlement) may be expressed as a fraction,
η
w
, of the sum of the
individual pile stiffnesses,
k
. Thus for a group of
n
piles
K
g
=
η
w
nk
(5.17)
Butterfield and Douglas showed that plotting the efficiency,
η
w
, against the number of
piles in a group gave essentially straight lines on logarithmic axes. The precise layout
of the piles appeared to have little influence on the computed efficiency, rectangular
groups of piles having the same efficiency as square groups at the same pile spacing.
The results from Figure 5.8 have been replotted as efficiencies in Figure 5.9. For
typical pile spacing of
s
/
d
∼
3 to 5, the resulting trends are linear in logarithmic space,
and may be represented by
n
−
e
n
1
−
e
k
η
w
∼
or
K
g
∼
(5.18)
with values of the exponent,
e
, typically in the range 0.5 to 0.6.
The results in Figures 5.8 and 5.9 have been obtained using the program PIGLET
(see following section) for groups of up to 900 piles (30
30), based on the interaction
approach of Mylonakis and Gazetas (1998). For large pile groups, the efficiency of
each pile falls to 0.05 and lower, indicating that each pile is only 5% as stiff as it
would be as an isolated pile. Thus a few widely spaced piles may be nearly as stiff as
many more closely spaced piles. For example, a group of 300 piles at
s
×
/
d
=
3 has an
efficiency of 0.03, or an overall stiffness equivalent to 400
×
0
.
025
=
10 isolated piles.
A group of 36 piles at
s
10 (covering approximately the same ground area) has
an efficiency of 0.1, or an overall stiffness equivalent to just under 4 isolated piles.
Reducing the number of piles by an order of magnitude gives a group stiffness that is
nearly 40% as high.
Natural soils exhibit non-linear response below yield, with the secant modulus
reducing from a maximum value,
G
0
, at small strains to much lower values at strain
/
d
=
